Spin-orbit interaction is the interaction of an electron's spin with the magnetic moment generated by the orbital motion of the electron. Or, from the point of view of an electron, it is the interaction between electron's spin and orbital motion of the nucleus.
And, for different atoms, the spin-orbital splitting of energy levels was found to be different. And the trend is that for heavier atoms the splitting is larger. I do not completely see why is that so qualitatively… Let's consider only the valence electrons. The heavier the atom, the more electrons it has and the more electrons are there in between the valence electrons and the nucleus, and the more efficient the screening effect. The last, as I understand, means that the Coulomb interaction between the valence electrons and the nucleus is largely reduced. And reduction is larger for the heavier elements. But larger spin-splitting should mean stronger interaction, right?
So why is the spin-orbit splitting larger in heavier atoms?
[Physics] Why is spin-orbit splitting larger in heavier atoms
atomic-physicsatomsquantum mechanicsquantum-spinspectroscopy
Best Answer
Some insight into this question may be gained from considering calculations of the spin orbit splitting $\Delta$ by F. Herman et al., Phys. Rev. Letts. $\textbf{11}$, 541 (1963), which I have plotted below. There we see a saw-tooth dependence of $\Delta$ with atomic number $Z$, with $\Delta = 0$ for a single valence electron in an outer shell (alkali metals) to a maximum for an electron in a full shell (inert gases).
This suggests that it is only the core electrons that screen the nucleus, with little or no screening of a valence electron by other electrons in the outer shell. For a given row of the periodic table, the number of screening core electrons will stay the same as $Z$ increases, so the local electric field seen by the electron will indeed increase with the size of the atom and hence give rise to a stronger spin-orbit splitting.